Answer :
Option C: ∠2 and ∠8
Option E: ∠3 and ∠5
Solution:
Two parallel lines cut by a transversal.
Option A: ∠5 and ∠4
∠4 is not interior of parallel lines.
Hence it is not true.
Option B: ∠6 and ∠5
∠6 is not interior of parallel lines.
Hence it is not true.
Option C: ∠2 and ∠8
∠2 and ∠8 lies in the interior of the parallel lines.
∠2 and ∠8 lies in alternate of the transversal line.
Therefore, ∠2 and ∠8 are alternate interior angles.
Hence it is true.
Option D: ∠8 and ∠1
∠1 is not interior of parallel lines.
Hence it is not true.
Option E: ∠3 and ∠5
∠3 and ∠5 lies in the interior of the parallel lines.
∠3 and ∠5 lies in alternate of the transversal line.
Therefore, ∠3 and ∠5 are alternate interior angles.
Hence it is true.
Therefore ∠2 and ∠8, ∠3 and ∠5 are alternate interior angles.
Alternate Interior angles are on the opposite side. The Pair of angles that are alternate interior angles are ∠2 and ∠8, ∠3 and ∠5.
What are Alternate Interior angles?
When two parallel lines are cut by a transverse. the angles formed on the interior of the parallel lines, on the opposite sides of the transverse are known as the Alternate Interior Angle.
In the given figures, the angles that are formed on the inner side of the two parallel lines are ∠2, ∠3, ∠8, and ∠5. Since, for a pair of angles to be alternate interior angles, they must be on the opposite side of the transverse. Therefore, ∠2 and ∠8, ∠3 and ∠5 are the two pairs of alternate interior angles.
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